Find coefficient of restitution

A question is this type if and only if it asks to determine the coefficient of restitution from given information about velocities before and after a collision.

4 questions · Challenging +1.6

6.03b Conservation of momentum: 1D two particles
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Pre-U Pre-U 9795/2 2012 June Q10
12 marks Challenging +1.8
10 \includegraphics[max width=\textwidth, alt={}, center]{d8ca5464-435f-45e0-8e19-1830415a7c60-5_432_949_258_598} A smooth sphere \(P\) of mass \(3 m\) is at rest on a smooth horizontal table. A second smooth sphere \(Q\) of mass \(m\) and the same radius as \(P\) is moving along the table towards \(P\) and strikes it obliquely (see diagram). After the collision, the directions of motion of the two spheres are perpendicular.
  1. Find the coefficient of restitution.
  2. Given that one sixth of the original kinetic energy is lost as a result of the collision, find the angle between the initial direction of motion of \(Q\) and the line of centres.
Pre-U Pre-U 9795/2 2016 Specimen Q11
12 marks Challenging +1.8
11 \includegraphics[max width=\textwidth, alt={}, center]{c4bbba86-2968-4247-b300-357217cf213b-5_432_949_909_557} A smooth sphere \(P\) of mass \(3 m\) is at rest on a smooth horizontal table. A second smooth sphere \(Q\) of mass \(m\) and the same radius as \(P\) is moving along the table towards \(P\) and strikes it obliquely (see diagram). After the collision, the directions of motion of the two spheres are perpendicular.
  1. Find the coefficient of restitution.
  2. Given that one-sixth of the original kinetic energy is lost as a result of the collision, find the angle between the initial direction of motion of \(Q\) and the line of centres.
Pre-U Pre-U 9795/2 2020 Specimen Q11
5 marks Challenging +1.8
11 \includegraphics[max width=\textwidth, alt={}, center]{f4acd242-eb78-4124-bfa2-fdecaa188690-6_438_953_264_557} A smooth sphere \(P\) of mass \(3 m\) is at rest on a smooth horizontal table. A second smooth sphere \(Q\) of mass \(m\) and the same radius as \(P\) is moving along the table towards \(P\) and strikes it obliquely (see diagram). After the collision, the directions of motion of the two spheres are perpendicular.
  1. Find the coefficient of restitution.
  2. Given that one-sixth of the original kinetic energy is lost as a result of the collision, find the angle between the initial direction of motion of \(Q\) and the line of centres.
CAIE FP2 2014 November Q2
5 marks Standard +0.8
\includegraphics{figure_2} A small smooth ball \(P\) is moving on a smooth horizontal plane with speed \(4\text{ m s}^{-1}\). It strikes a smooth vertical barrier at an angle \(\alpha\) (see diagram). The coefficient of restitution between \(P\) and the barrier is \(0.4\). Given that the speed of \(P\) is halved as a result of the collision, find the value of \(\alpha\). [5]